A semi-empirical correlation energy for nuclei

A semi-empirical interaction is used to calculate higher order corrections to the binding energies of even—even nuclei close to the line of stability. These corrections are taken to come from two phonon configurations and are treated as a perturbation with respect to the BCS nuclear ground state which is obtained from applying the energy density method to finite nuclei. The overall correspondence between theory and experiment for the 60 nuclei calculated between A =52 and A =234 is good, with excellent agreement for the non-deformed nuclei situated within the regions A = 72 to 144 and A = 200 to 212. The large correction enegies (several MeV per nucleus on the average) indicate that these correlations are of importance for explaining nuclear binding energies and that it is necessary to include them within energy functional itself. The fact that these correlations come almost exclusively from nucleons close to the fermi surface is also discussed.     

Semi-microscopic calculation of the level density in spherical nuclei

The level density at the neutron binding energy for 90 spherical nuclei in the interval 50 < A < 205 is calculated by a method of direct counting of the number of states taking into account collective vibrational excitations. The results of calculations are in satisfactory agreement with the experimental data. The difference in the level density of doubly even and odd-A nuclei is correctly described. The effect of nuclear vibrations on the level density is studied, and it is shown that the account of them leads to an increase in the density by a factor of 1.5–10 and to a decrease in the density fluctuations. It is also studied how the level density depends on excitation energy. With increasing excitation energy, our results come nearer the corresponding values obtained by the statistical model. It is found that the density fluctuations decrease with increasing excitation energy but remain still strong at the neutron binding energy for nuclei with A = 50–70 and for nuclei around closed shells. The density ρ(I^π) is studied as a function of spin and parity. It is shown that at the neutron binding energy the ratio $\text{ρ(I}{}^{\mathrm{+}}\text{)}\text{ρ(I}{}^{\mathrm{?}}\text{)}$ is different from unity for the majority of nuclei. This difference is especially striking for ⁵⁷Fe and ⁵⁸Fe nuclei.     

New perspectives on the level density of compound resonances

The level density of compound resonances observed at neutron separation energy is subject of closer investigation and interpretation. The structures in the level density parameter as a function of the mass number allow the determination of the hierarchy of the compound states and the definition of a base line which represents the level density parameter of spherical nuclei with no residual interaction and no shell effects. Using the base line a method becomes available enabling the separation of the residual interaction from properties of the average potential defined in the framework of the shell model. The following examples in different mass regions are discussed: the change of the pairing energy due to the blocking effect atA ≈ 70; the breakdown of the pairing correlation atA ≈ 105 is interpreted as neutron-proton interaction; similar effects in the mass region 150<A<170 are discussed with neutron-proton interaction and the backbending phenomen. Finally it will be shown that there is no enhancement of states due to collective properties of nuclei at high excitation energy.     

Nuclide yields of light fission products from thermal-neutron induced fission of 233U at different kinetic energies

The yields of light fission products from thermal-neutron induced fission of ²³³U are measured as a function of their mass A, their nuclear charge Z, their kinetic energy E and their ionic charge state q at the recoil spectrometer Lohengrin of the Institut Laue-Langevin in Grenoble. The mass yields are determined by intercepting the fragments with an ionization chamber of high energy resolution positioned at the focal plane of the spectrometer. The nuclear charges and their yields are determined with the same ionization chamber by measuring the residual energy of fission products, selected monoenergetically by Lohengrin, behind a passive absorber made of parylene-C. The nuclear charge resolution enabled by this detector device is considerably improved to Z/dZ = 58. The nuclear charge and mass distributions summed over all ionic charge states are listed within the mass range 79 ⩽ A ⩽ 106 at 6 energies: E = 85.34, 90.41, 95.46, 100.50, 105.55 and 110.55 MeV. The energy-integrated nuclear charge and mass yields are also given. The isotonic and isotopic yields are shown. An odd-even effect in the yields is found for the protons as well as for the neutrons at all kinetic energies. The yield weighted total odd-even effect for the protons is found to be (22.1 ± 2.1)%, for the neutrons (5.4 ± 1.7)%. An odd-even effect for the protons in the mean kinetic energy is also observed. The displacement of the mean isobaric nuclear charges from the unchanged charge-density values and the variances of the isobaric nuclear-charge distributions reveal fine structures in their mass dependences.     

Partial level density of n-quasiparticle excitations, radiative strength functions and new experimental information on the dynamics of nuclear structure change in the B n range

The most reliable at present values of the level density in the fixed spin window and the sums of radiative strength functions of cascade gamma transitions are obtained from analysis of intensities of two-step cascades excited upon thermal neutron capture for approximately 40 nuclei in the mass range 40 ≤ A ≤ 200. The maximal reliability of these data is provided by the experimental conditions—minimum possible propagation error coefficients and practically unique solution of the problem of determination of gamma decay parameters from measured spectra. The experimental data are approximated by the sum of partial level densities corresponding to excitation of n quasiparticles. Steplike structures in the level density at excitation energies smaller than 3–4 MeV are described with good accuracy as the superposition of two-quasiparticle (three-quasiparticle in odd A nuclei) and vibrational excitations with the coefficient of collective density enhancement K _coll ≈ 10?20. They correspond to excitation-energy-correlated maximum enhancement of the radiative strength functions of primary gamma transitions. The level density at larger excitation energies is well reproduced if the breakup of at least two more Cooper pairs of nucleons is taken into account. The increase in the number of excited quasiparticles in the nucleus corresponds to unconditional reduction of the radiative strength functions of primary gamma transitions of the compound state decay. However, the maximum possible value of partial widths of primary transitions increases regularly with decreasing energy. Some ambiguity in the results of approximation and divergence from existing theoretical ideas of the energy dependence of nucleon correlation functions in an excited nucleus point to the possibility of direct extraction from experiment of fundamentally new information on the structure of excited nuclear levels in the range of the neutron binding energy. These are, first of all, the parameters of dependence of nucleon correlation functions on the excitation energy of the nucleus.     

The Fourth-Order Symmetry Energy of Finite Nuclei

The fourth-order symmetry energy E_sym,4(A) of heavy nuclei is investigated based on the Skyrme energy density functional in combination with a local density approximation. Unlike some previous works, in our method, the interferences from the other energy terms are removed since it is completely isolated from the rest of energy terms. The calculated E_sym,4(A) is much less than that extracted from nuclear masses. The underlying reason for the big difference is discussed. The Brueckner theory also gives a small fourth-order symmetry energy coefficient of nuclear matter, which is also different from recent conclusions with another methods.     

Reaction cross sections in Si of light proton-halo candidates 12N and 17Ne

Total reaction cross sections, σ_R, on Si were measured near 40 A MeV for the proton-halo candidate ¹²N and the two-proton-halo candidate ¹⁷Ne, and were compared with σ_R for other light proton-rich nuclei. The A-dependence shows enhanced σ_R's for ¹²N and ¹⁷Ne, relative to their neighbors, but the effect is smaller than for ⁸B which has been argued to have a proton halo. In general, nuclei with loosely bound last protons (S_p ⩽ 1.5 MeV) have significantly larger σ_R's than their neighbors. Cross sections for charge-removal from ¹²N and ¹⁷Ne also were obtained.     

Core polarization and Coulomb displacement energies

A systematic study of the core polarization correction to Coulomb displacement energies is carried out. A zero range density independent and density dependent force is used to calculate this correction in the A = 16, A = 40, and A = 208 regions. It is found that the core polarization correction does not increase the Coulomb displacement energies and, therefore, cannot resolve the existing discrepancy between theory and experiment. Moreover, when the mean square radius of the excess neutron distribution is decreased the core polarization correction to the Coulomb energy becomes attractive and cancels the gain resulting from the direct Coulomb term. Hence, it is concluded that the discrepancy cannot be resolved even when the excess neutron distribution has an anomalously small radius. It is also pointed out that when the core polarization term is added the discrepancy is almost equal in mirror nuclei with a single hole in the N = Z core and those with a single particle outside the same core. Evidently, additional charge asymmetric corrections are required to resolve the discrepancies in Coulomb displacement energies.     

Shell structure and stability of nuclei with 270<A<500 and the possible existence of primordial superheavy nuclei

The self-consistent energy density method is applied to the study of the properties of superheavy nuclei with 270<A<500. The shell structure,α-decay energy andα-decay half-life are predicted for the heaviestβ-stable isotope of each even element. The characteristics of nuclear densities and single-particle potentials in the superheavy region are also examined, with a particular attention on the surface diffuseness. After an approximate calculation of their fission barrier heights, only a few heavy isotopes of elements 106 and 108 are predicted to have a small chance to be found in nature. Their possible formation by ther-process is discussed.     

Breathing cluster model for nuclei of two s-wave clusters

A microscopic cluster model with a pair of breathing clusters and an interaction that reproduces the correct energies and radii of the separate clusters is applied to the nuclei with 5⩽A⩽8. The energies are well reproduced, and, as shown by the charge form factor and αd fragmentation strength of ⁶Li, the low-momentum behaviour of the wave functions is also realistic.     

On the surface energy of compressible nuclei

The specific nuclear surface energy σ as a function of the central density n_c is shown to behave in a way opposite to that of the saturation curve; in particular, σ is maximum at the saturation density. Starting from the energy of a compressible nucleus, we find after deriving a simple expression for the second derivative of σ, a formula for thecompressibility modulus K_A of finite nuclei which contains, besides the saturation density and the bulk value K_∞, only some well-known surface parameters.     

Properties of alpha-particle solutions to the many-nucleon problem

A class of A-nucleon (for even N = Z) Hamiltonians is found such that they admit, among others, solutions that can be exactly related to solutions to the problem of A/4 alpha particles in the sense that the respective eigenvalues of the two problems coincide and that the A-nucleon solutions can be constructed from the alpha-particle solutions within a procedure that follows from the resonating-group model. It is shown that an effective nuclear Hamiltonian close to a realistic one possesses these properties, the alpha-particle states in nuclei having basic properties of an alpha condensate and, frequently, a normal nuclear density. The statistics of alpha particles (and other composite bosons) proves to be different from Bose-Einstein and Fermi-Dirac statistics and from parastatistics.     

Supplement to energy levels of A = 21–44 nuclei (VII)

The experimentally determined properties of A = 21–44 nuclei are compiled and evaluated with special emphasis on nuclear spectroscopy. The present paper, a supplement to the most recent complete A = 21–44 review (90En08), mainly discusses the new data published in the period 1990–1996, and thus can only be used in conjunction with 90En08. The set-up and notation are identical with those of 90En08. Data selection for the supplement, however, is more restricted. Only data are taken along concerning discrete nuclear states with the consequence that papers on reaction mechanisms or on states in the high-energy continuum are disregarded. A novelty in the supplement is the inclusion of a comparison of π = +, T⩽2 states with the shell model (untruncated sd shell).     

Isospin symmetry and giant resonance in nuclei of mass number <Emphasis Type="Italic">A</Emphasis> = 14

An analysis of the cross sections for photon absorption by isobar nuclei ¹⁴C and ¹⁴N in the giant-dipole-resonance region demonstrates a high degree of isospin symmetry for this type of collective excitations in the above nuclei. Giant resonances in A = 14 isobar nuclei are related by a simple rescaling procedure that is based on the fact that, for these nuclei, the isospin remains a good quantum number in the process of dipole excitations of energy up to about 40 MeV. The features of the isospin splitting of the giant resonance in the ¹⁴C nucleus are refined. The shape of the cross section for photoabsorption in the ¹⁴C nucleus—in particular, a large width of the giant resonance in this nucleus—is exhaustively explained.     

The breaking of intrinsic reflection symmetry in nuclear ground states

Negative-parity excited states of doubly even nuclei have earlier been attributed to vibrational excitations. This paper shows that an interpretation starting from a reflection asymmetric intrinsic state is more appropriate for certain nuclei in the radium region. Theoretical evidence for stable octupole deformation comes from a deformed shell-model calculation in which we use a single-particle potential with a realistic radial shape and a finite-range interaction for the surface energy. The octupole effect systematically improves the agreement between theoretical and experimental masses. The low-lying O⁺ excitations observed in experiment are compatible with the calculated collective octupole potentials. The possibility of obtaining further evidence from the spectroscopy of odd-mass nuclei is considered in an exactly solvable model, which shows that the smaller energy splitting observed in odd-A parity doublets mainly reflects single-particle fragmentation of the collective mode. The systematics of theoretical shell structure and experimental spectroscopy suggests the presence of other regions of octupole collectivity near the limits of stability.     

Microscopic calculation of pre-equilibrium emission

Previous TDHF calculations have shown that a pre-equilibrium emission of nucleons should be seen for asymmetric collisions of nuclei. Recent calculations indicate that the added effect of two-body collisions is to enhance this pre-equilibrium emission, it being seen also for symmetric collisions. More detailed calculations of this phenomenon are presenied here. The two-body collisions are treated by the time-relaxation method. This method is reviewed, and a revised formula for the relaxation time is introduced.Calculations are made in a slab geometry. For real nuclei, as much as 6% of all nucleons are estimated to be emitted at a beam energy of E_c.m. = 20 MeV/A. The energy distribution of the emitted nucleons relates to a temperature of 13 MeV at this energy. At 5 MeV/A, the emission is reduced to about 1 %.     

Decay of heavy and superheavy nuclei

We present here, an overview and progress of the theoretical works on the isomeric state α decay, α decay fine structure of even–even, even–odd, odd–even and odd–odd nuclei, a study on the feasibility of observing α decay chains from the isotopes of the superheavy nuclei Z = 115 in the range 271 ≤A ≤ 294 and the isotopes of Z = 117 in the range 270 ≤A ≤ 301, within the Coulomb and proximity potential model for deformed nuclei (CPPMDN). The computed half-lives of the favoured and unfavoured α decay of nuclei in the range 67 ≤Z ≤ 91 from both the ground state and isomeric state, are in good agreement with the experimental data and the standard deviation of half-life is found to be 0.44. From the α fine structure studies done on various ranges of nuclei, it is evident that, for nearly all the transitions, the theoretical values show good match with the experimental values. This reveals that CPPMDN is successful in explaining the fine structure of even–even, even–odd, odd–even and odd–odd nuclei. Our studies on the α decay of the superheavy nuclei ^271?294115 and ^270?301117 predict 4 α chains consistently from ^284,285,286115 nuclei and 5α chains and 3α chains consistently from ^288?291117 and ²⁹²117, respectively. We thus hope that these studies on ^284?286115 and ^288?292117 will be a guide to future experiments.     

On the deviation of small nuclear systems from saturation

Below a definite thickness, the structure of nuclear slabs — treated in the energy density formalism — deviates from saturation, and in particular the surface tension decreases rapidly. These effects, seemingly a consequence of the finite range of nuclear forces, cannot be accounted for by the droplet-model concept. A (negative) correction term is proposed for the nuclear mass formula which becomes important for small nuclei in addition to the (positive) curvature energy. Its consideration may remove ambiguities in theoretical predictions and empirical values of the curvature energy.     

Über die Anwendung von Greenfunktionen zur Beschreibung von Paarungseffekten bei deformierten Atomkernen

The theory of nuclear pairing correlations, recently developed byMigdal, introduces only one constant, which should be nearly the same for all nuclei. This Green's function method is compared with the well known BCS-theory. The constant is fitted and the problem has been solved by numerical methods. We found that the constant varies likeA ^?1/2. The individual magnitude of the pairing energy depends strongly on the single particle level density which determines the value of the renormalized coupling constant of the pairinteraction. This enables us to reproduce the deviations of the pairing energy from the curveδ _n =11,2A ^?1/2. The results are independent from the choice of the cut-off level.